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What is mathematics?


ajb
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Expanding on and paraphrasing the @MigL's statement above:

As a mathematician, "I'm not overly concerned with the 'why' of a paradigm, or set of rules, only its 'function'."

"Math is simply a tool for describing/investigating the world" of absolute truths, which are independent of the world around us and thus hold and can be trusted when investigating new, unfamiliar worlds.

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50 minutes ago, joigus said:

But I don't disagree with this. In fact:

Let me add another definition of maths that I've heard to Marcus du Sautoy, if I remember correctly:

Maths is the study of patterns

Yes, I think he did say that, or something very like it.
Did you read his delightful book on symmetry containing references to his visit to the Alhambra ?

 

The interesting thing about patterns is that they can be algebraicised for incidence using incidence matrices.

Another related point is that in studying patterns maths uses much the same techniques as other disciplines.
In particular idealisations are extracted from observations of reality, many of these idealisations are also of great use in Physics.

Another author much concerned with pattern is Philip Ball  - The self Made Tapestry.

Di you know the pattern to determine the optimum level to fill a cement mixer ?

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7 hours ago, studiot said:

Yes, I think he did say that, or something very like it.
Did you read his delightful book on symmetry containing references to his visit to the Alhambra ?

 

The interesting thing about patterns is that they can be algebraicised for incidence using incidence matrices.

Another related point is that in studying patterns maths uses much the same techniques as other disciplines.
In particular idealisations are extracted from observations of reality, many of these idealisations are also of great use in Physics.

Another author much concerned with pattern is Philip Ball  - The self Made Tapestry.

Di you know the pattern to determine the optimum level to fill a cement mixer ?

I know du Sautoy from the documentaries. 'The Self-Made Tapestry' does ring a bell, perhaps you mentioned it before.

I have no idea about cement mixer patterns, but sounds interesting.

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51 minutes ago, joigus said:

I know du Sautoy from the documentaries. 'The Self-Made Tapestry' does ring a bell, perhaps you mentioned it before.

I have no idea about cement mixer patterns, but sounds interesting.

Du Sautoy is definitely into symmetry. He has written at least three books.

The Alhambra stories are in the Finding Moonshine one.

https://www.amazon.co.uk/Symmetry-Journey-Into-Patterns-Nature/dp/0060789417

 

Here are the relevent pages from Ball's Tapestry about mixing drums.

My apologies for the poor scans due to the spine of the book.

mixer1.thumb.jpg.9784351601570f02ca9627f1cf2b0ea7.jpgmixer2.thumb.jpg.edd31dfa0366a7f29bf33afa921e807f.jpg

 

Edited by studiot
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